This was my reply to the first post that I came across that looked just like this one. Looking back, maccadon apologized for putting it first in the wrong area.

Save the flies by drying them out ASAP.
Some fly boxes may not allow enough air to get to the hooks before they can start rusting. Boxes in which the flies are held by foam are notorious for this. In this case take the flies out of the boxes to let them dry.
To speed things up you can blot most of the moisture out with paper towling. If the flies looks mushed after they dry, steam them over a tea pot to pop the materials back into shape. Of course after that you should let them air dry again before stashing them back into a dry fly box.
All is not lost if you dry them as quickly as possible after they're dunked.